Book:J. David Logan/A First Course in Differential Equations
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J. David Logan: A First Course in Differential Equations
Published $\text {2005}$, Springer
- ISBN 978-1441975911
Subject Matter
Contents
- Preface
- To the Student
- 1. Differential Equations and Models
- 1.1 Differential Equations
- 1.1.1 Equations and Solutions
- 1.1.2 Geometrical Interpretation
- 1.2 Pure Time Equations
- 1.3 Mathematical Models
- 1.3.1 Particle Dynamics
- 1.3.2 Autonomous Differential Equations
- 1.3.3 Stability and Bifurcations
- 1.3.4 Heat Transfer
- 1.3.5 Chemical Reactors
- 1.3.6 Electric Circuits
- 1.1 Differential Equations
- 2. Analytic Solutions and Approximations
- 2.1 Separation of Variables
- 2.2 First-Order Linear Equations
- 2.3 Approximation
- 2.3.1 Picard Iteration
- 2.3.2 Numerical Methods
- 2.3.3 Error Analysis
- 3. Second-Order Differential Equations
- 3.1 Particle Mechanics
- 3.2 Linear Equations with Constant Coefficients
- 3.3 The Nonhomogeneous Equation
- 3.3.1 Undetermined Coefficients
- 3.3.2 Resonance
- 3.4 Variable Coefficients
- 3.4.1 Cauchy–Euler Equation
- 3.4.2 Power Series Solutions
- 3.4.3 Reduction of Order
- 3.4.4 Variation of Parameters
- 3.5 Higher-Order Equations
- 3.6 Summary and Review
- 4. Laplace Transformations
- 4.1 Definition and Basic Properties
- 4.2 Initial Value Problems
- 4.3 The Convolution Property
- 4.4 Discontinuous Sources
- 4.5 Point Sources
- 4.6 Table of Laplace Transformations
- 5. Linear Systems
- 5.1 Introduction
- 5.2 Matrices
- 5.3 Two-Dimensional Systems
- 5.3.1 Solutions and Linear Orbits
- 5.3.2 The Eigenvalue Problems
- 5.3.3 Real Unequal Eigenvalues
- 5.3.4 Complex Eigenvalues
- 5.3.5 Real, Repeated Eigenvalues
- 5.3.6 Stability
- 5.4 Nonhomogeneous Systems
- 5.5 Three-Dimensional Systems
- 6. Nonlinear Systems
- 6.1 Nonlinear Models
- 6.1.1 Phase Plane Phenomena
- 6.1.2 The Lotka-Volterra Model
- 6.1.3 Holling Functional Responses
- 6.1.4 An Epidemic Model
- 6.2 Numerical Methods
- 6.3 Linearization and Stability
- 6.4 Periodic Solutions
- 6.4.1 The Poincaré-Bendixson Theorem
- 6.1 Nonlinear Models
- Appendix A. References
- Appendix B. Computer Algebra Systems
- B.1 Maple
- B.2 MATLAB
- Appendix C. Sample Examinations
- Appendix D. Solutions and Hints to Selected Exercises
- Index